Transitioning to California's Common Core Content Standards for ...

Transitioning to California’s 

Common Core 

Content Standards 

for Grade 4 

with 

Pearson

Grade 4 

Table of Contents 


Transitioning to a Common Core Classroom 

with enVisionMATH ® California....................................................................................................... 2 

Standards for Mathematical Content — Grade 4 Overview .........................................................3 

Standards for Mathematical Practice...............................................................................................7 

Correlation of California’s Common Core Content Standards 

to enVisionMATH California Grade 4 ............................................................................................13 

Pacing for a Common Core Curriculum with enVisionMATH California ................................19 

Listing of Supplemental Common Core Lessons.........................................................................29 

   

Grade 4 



Transitioning to a Common Core Classroom 

with enVisionMATH ® California....................................................................................................... 2 

California’s Common Core Content Standards— Grade 4 Overview ......................................... 3 

Standards for Mathematical Practice...............................................................................................7 


to enVisionMATH California Grade 4 ............................................................................................13 

Pacing for a Common Core Curriculum with enVisionMATH California ................................19 

Listing of Supplemental Common Core Lessons.........................................................................29 

   

Grade 4 

Transitioning to a Common Core Curriculum 

Transitioning to a Common Core Curriculum 

with enVisionMATH® California 

Pearson is committed to supporting California teachers as they transition to a mathematics 

curriculum that is based on California’s Common Core Content Standards for Mathematics. 

This commitment includes not just curricular support, but also professional development 

support to help members of the education community gain greater understanding of the 

new standards and of the expectations for instruction. 

With this guide, we offer overview information about both the Standards for Mathematical 

Content and for Mathematical Practice, the two sets of standards that make up California’s 

Common Core Content Standards for Mathematics. In the Overview of the Standards for 

Mathematical Content, teachers can become aware of critical shifts in content or 

instructional focus in the new standards as they begin planning a Common Core-based 

curriculum. In the Standards for Mathematical Practice essay, we present the features and 

elements of Scott Foresman Addison Wesley enVisionMATH California ©2009 that provide 

students with opportunities to meet these standards and develop mathematical proficiency. 

You will also find a correlation of enVisionMATH California ©2009 Grade 4 to California’s 

Common Core Content Standards for Mathematics – Grade 4. The correlation includes the 

supplemental lessons that will be made available to ensure comprehensive coverage of all 

of content standards for Grade 4. Additionally, we have included Pacing for a Common 

Core Curriculum, a pacing guide that recommends when each of the supplemental lessons 

should be taught. Look for the lessons with a lower case letter as part of the lesson number 

(i.e., 4-3a, 8-8b). 

Finally, we offer a listing of the supplemental lessons that will be made available summer 

2011. These lessons maintain the successful instructional approach of the enVisionMATH 

California ©2009, while highlighting the connections to the Standards for Mathematical 

Practice.   

2

Grade 4 

Grade 4 Overview 

California’s Common Core Content Standards 

Grade 4 Overview 

Main Areas of Emphasis 

• Multi-digit multiplication and concepts of division with multi-digit dividends 

• Fraction equivalence and operations (addition, subtraction, and multiplication) with 

fractions and whole numbers 

• Analysis and classification of two-dimensional shapes based on properties and attributes 

Students extend their study of multiplication to four-digit numbers by one- and two-digit 

numbers. Drawing on their understanding of models of multiplication developed in Grade 3, 

students develop strategies and methods to find products of multi-digit whole numbers. 

Students also build on their conceptual understanding of division, place value, properties of 

operations, and the relationship between multiplication and division to develop procedures to 

find quotients involving multi-digit dividends. 

Students build on their understanding of unit fractions and fraction equivalence to compare 

fractions with different numerators and denominators. They extend their understanding of 

operations and unit fractions to add and subtract fractions with like denominators, and use 

visual representations to explain their work; for example, they decompose fractions into the sum 

of unit fractions to add and subtract fractions and mixed numbers with like denominators. 

Further, they draw from their understanding of multiplication and unit fractions as they explore 

multiplying fractions and whole numbers. 

Grade 4 students extend their understanding of the properties of two-dimensional shapes by 

describing and analyzing shapes, looking in particular at the angles and lines of shapes to 

categorize them (e.g., triangles, quadrilaterals). Students also explore line symmetry. 

3 

Grade 4 

Standards for Mathematical Content 

New Approaches to Content in Grade 4 

The Common Core State Standards for Mathematics promote the development of not just 

conceptual and procedural understandings of operations, but also an analytic framework from 

which students begin to see patterns in the way operations function. In Grade 4, students 

formalize their understanding of the standard algorithm for multiplication and division. They 

explore another meaning of multiplication: as comparison; for example, one student has five 

times as many pencils as another student. They analyze the multiplicative comparison and the 

additive comparison. Students interpret remainders of division problems to maintain a 

contextual meaning for the operations. 

As students develop fluency with multiplication, they explore another classification of numbers 

as factors and multiples. They find all factor pairs for whole numbers to 100 and identify 

numbers as multiples of a single-digit number. Students classify numbers as prime or 

composite. 

In Grade 4, students begin a formal study of patterns to lay a foundation for algebraic thinking. 

Students generate patterns that follow a rule and describe the pattern, identifying features of the 

pattern that are not explicit to the rule itself. Students also begin to represent problem situations 

with equations that include a letter or symbol to represent an unknown as part of the foundation 

for algebraic thinking. 

The Common Core State Standards recommend using the unit fraction to build students’ 

knowledge of fractions. In Grade 4, addition and subtraction of fractions grow from composing 

unit fractions into fractions and decomposing fractions to unit fractions. Similarly, students’ 

work with multiplying fractions begins with the understanding of a fraction as a multiple of a 

unit fraction, with special attention to the size of the whole. This contextualization of fractions to 

the parts of the wholes that they represent is an important concept in the study of fractions. 

Students realize while ½ always represents one half of a whole, the halves are not equal if the 

whole are different sizes. 

Students’ work with data displays integrates their study of fractions. They make line plots with 

the horizontal scale marked off in halves, fourths, and eighths and solve problems involving 

addition and subtraction of fractional values presented on the line plots. 

Students extend their study of place value and rounding to 1,000,000 in Grade 4. They formalize 

the relationship among the places in a multi-digit number (i.e., power of 10). Further, they 

express numbers in different forms: using base-ten numerals (standard form), number names 

(word form) and expanded form. They achieve fluency with multi-digit addition and 

subtraction. 

4 

Grade 4 


Important Progressions across Grades 

Grade 4 students continue the study of multiplication and division that they started in Grade 3. 

They expand their understandings of the meaning of multiplication to include multiplication as 

comparison (e.g., 5 times as many objects) and distinguish between multiplicative comparison 

and additive comparison (e.g., 5 more). Student multiply multi-digit numbers, using strategies 

based on place value and properties of operations, and provide visual explanations of their 

calculations (e.g., area models, rectangular arrays). By Grade 5, students will achieve fluency 

with multi-digit multiplication using the standard algorithm. 

Grade 4 students carry out multi-digit division calculations with dividends up to four digits and 

one-digit divisors. They use strategies based on place value, properties of operations, and the 

inverse relationship between multiplication and division. As they did with multiplication 

calculations, students explain their solutions to division problems using visual models or 

equations. Students also interpret remainders, explaining the meaning for each problem 

context. In Grade 5, students will find quotients of division problems with four-digit dividends 

and two-digit divisors and in Grade 6, will achieve fluency with multi-digit whole number 

division using the standard algorithm. 

Students began their formal study of fractions in Grade 3, with an emphasis on unit fractions 

and their representation on the number line. In Grade 4, students focus on equivalence of 

fractions and compare fractions using visual models. They apply their knowledge of unit 

fractions and fraction equivalence to compare fractions with different numerators or 

denominators. Grade 4 students draw from their understanding of operations and fraction 

equivalence to add and subtract fractions and mixed numbers with like denominators. In Grade 

5, they will extend these operations to fraction with unlike denominators. Students will explore 

multiplying fractions by whole numbers to ground their understanding in the meaning of the 

operation. In Grade 5, students will multiply fractions and fractions, and explore division of 

fractions by whole numbers and vice versa. By Grade 6, students become fluent with all 

operations involving fractions, including decimal fractions. 

Grade 4 students begin their study of decimal fractions. They use decimal notation for fractions 

with denominators of 10 and 100, and compare decimals to hundredths. Grade 5 students 

undertake a comprehensive study of decimals. Starting with decimal place value, students read, 

write, and compare decimals to the thousandths. They apply their understandings of operations 

(addition, subtraction, multiplication, and division) with whole numbers to operations with 

decimals. By the end of Grade 6, they have mastered operations with decimals. 

Grade 4 students draw from the measurement concepts and skills developed in earlier years to 

solve problems involving distance (linear measure from Grades 1 through 3), time intervals 

(Grades 1 and 2), liquid volume (Grades 2 and 3), mass (Grades 2 and 3), and money (Grade 2). 

Students know the relative sizes of units of measurement and can express unit measurements 

from a larger in terms of a smaller unit. 

In Grade 4, students continue to build on their reasoning on the attributes of shapes from 

Grades 1 through 3. They focus specifically on angles and lines. Students classify shapes based 

on the angles (right, acute, obtuse) and lines (perpendicular, parallel) that make up the shapes. 

Students also look for line symmetry in shapes as a defining attribute. 

5 

Grade 4 


What’s Different? 

Unlike many state curriculum frameworks, the Common Core State Standards do not present a 

spiral curriculum in which students revisit numerous topics from one year to the next with 

progressively more complex study. Rather, the CCSS identify a limited number of topics at each 

grade level, allowing enough time for students to achieve mastery of these concepts. The 

subsequent year of study builds on the concepts of the previous year. While some review of 

topics from earlier grades is appropriate and encouraged, the CCSS writers assert that 

reteaching of these topics should not be needed. 

Certain topics that have often been part of the Grade 4 curriculum are not included in the CCSS. 

Among the most noticeable are a pared-down set of geometry and data analysis standards, and 

the absence of probability concepts. Other topics, such as operations with fractions and 

decimals have been shifted to different grades. 

Number and Operations The study of decimals in Grade 4 is limited to an exploration of 

decimal fractions. Students undertake operations with decimals in Grade 5. Operations with 

fractions are limited to addition and subtraction with like denominators and multiplication of 

fractions and whole numbers. 

Measurement The study of temperature is not part of the CCSS. 

Geometry The CCSS introduce the study of congruence and transformations in Grade 8, and the 

study of coordinate grids begins in Grade 5. While students in Kindergarten through Grade 2 

explore three-dimensional shapes, compose them and compare and contrast them to twodimensional 

shapes, students do not revisit three-dimensional shapes until Grade 5 with the 

study of volume. 

Data Analysis Students represent data in picture or bar graphs in Grades 2 and 3, but have 

limited experiences with other data displays except line plots. 

Probability Students first encounter probability concepts in Grade 7.   

6 

Grade 4 

Standards of Mathematical Practice 

Standards for Mathematical Practice 

Grade 4 

The Standards for Mathematical Practice are an important part of California’s Common Core 

Content Standards. They describe varieties of proficiency that teachers should focus on 

developing in their students. These practices draw from the NCTM process standards of 

problem solving, reasoning and proof, communication, representation, and connections and 

the strands of mathematical proficiency specified in the National Research Council’s report 

Adding It Up: adaptive reasoning, strategic competence, conceptual understanding, procedural 

fluency, and productive disposition. 

For each of the Standards for Mathematical Practice presented in the text that follows, is a 

explanation of the different features and elements of Pearson’s Scott Foresman • Addison Wesley 

enVisionMATH TM California that help students develop mathematical proficiency. 

1 Make sense of problems and persevere in solving them. 

Mathematically proficient students start by explaining to themselves the meaning of a problem and 

looking for entry points to its solution. They analyze givens, constraints, relationships, and goals. They 

make conjectures about the form and meaning of the solution and plan a solution pathway rather than 

simply jumping into a solution attempt. They consider analogous problems, and try special cases and 

simpler forms of the original problem in order to gain insight into its solution. They monitor and evaluate 

their progress and change course if necessary. Older students might, depending on the context of the 

problem, transform algebraic expressions or change the viewing window on their graphing calculator to 

get the information they need. Mathematically proficient students can explain correspondences between 

equations, verbal descriptions, tables, and graphs or draw diagrams of important features and 

relationships, graph data, and search for regularity or trends. Younger students might rely on using 

concrete objects or pictures to help conceptualize and solve a problem. Mathematically proficient 

students check their answers to problems using a different method, and they continually ask themselves, 

“Does this make sense? ”They can understand the approaches of others to solving complex problems 

and identify correspondences between different approaches. 

  

Scott Foresman • Addison Wesley enVisionMATH California is built on a foundation of problembased 

instruction that has sense-making at its heart. The Problem Solving Handbook, found on 

pages xviii-xxix, presents to students a 3-phase process that begins with making sense of the 

problem to solve. The first phase of the process has students ask themselves, What am I trying to 

find? What do I know? to help them identify the givens and constraints of a problem situation. In 

the second phase, the plan and solve phase, students decide on a solution plan. The Problem- 

Solving Recording Sheet, a reproducible teaching resource, provides students with a useful 

structured outline to help them become fluent with thinking about (making sense of) a problem 

and planning a workable solution pathway. 

The structure of each lesson facilitates students’ implementation of this process. Every lesson 

begins with Problem-Based Interactive Learning, an activity in which students are presented a 

problem to solve. They interact with their peers and teachers to make sense of the problem 

presented and to look for a workable solution. A second feature of each lesson are the Problem 

Solving exercises for which students persevere to find solutions for each exercise. In each topic 

is at least one Problem Solving lesson with a primary focus of honing students’ sense-making 

and problem-solving skills. 

7

Grade 4 


Throughout the program; for examples, see Grade 4 Lessons 1-3, 1-8, 2-1, 2-2, 2-3, 2-4, 2-5, 2-6, 

3-6, 4-6, 

5-5, 6-6, 10-6, 10-8, 12-11, 13-10, 14-4, 14-6, 14-9, 14-10, 14-11, 15-5 

2 Reason abstractly and quantitatively. 

Mathematically proficient students make sense of quantities and their relationships in problem 

situations. They bring two complementary abilities to bear on problems involving quantitative 

relationships: the ability to decontextualize—to abstract a given situation and represent it 

symbolically and manipulate the representing symbols as if they have a life of their own, without 

necessarily attending to their referents—and the ability to contextualize, to pause as needed during 

the manipulation process in order to probe into the referents for the symbols involved. Quantitative 

reasoning entails habits of creating a coherent representation of the problem at hand; considering 

the units involved; attending to the meaning of quantities, not just how to compute them; and 

knowing and flexibly using different properties of operations and objects. 

Scott Foresman • Addison Wesley enVisionMATH California program provides scaffolded 

instruction to help students develop both quantitative and abstract reasoning. In the Visual 

Learning Bridge students learn how to represent the given situation numerically or 

algebraically. Later in a lesson, students have opportunities to reason abstractly as they 

endeavor to represent situations symbolically. Throughout the solving process, students are 

reminded to check back to the problem situation with the Reasonableness exercises. In the Do 

You Understand part of the Guided Practice, students gain experiences with quantitative 

reasoning as they consider the meaning of different parts of an expression or equation. 

Throughout the exercise sets are Reasoning exercises that focus students’ attention on the 

structure or meaning of an operation rather than the solution. 


10-8, 11-3, 12-5, 13-6, 14-11, 15-5. 

8

Grade 4 


3 Construct viable arguments and critique the reasoning of 

others. 

Mathematically proficient students understand and use stated assumptions, definitions, and 

previously established results in constructing arguments. They make conjectures and build a logical 

progression of statements to explore the truth of their conjectures. They are able to analyze 

situations by breaking them into cases, and can recognize and use counterexamples. They justify 

their conclusions, communicate them to others, and respond to the arguments of others. They 

reason inductively about data, making plausible arguments that take into account the context from 

which the data arose. Mathematically proficient students are also able to compare the effectiveness 

of two plausible arguments, distinguish correct logic or reasoning from that which is flawed, and— 

if there is a flaw in an argument—explain what it is. Elementary students can construct arguments 

using concrete referents such as objects, drawings, diagrams, and actions. Such arguments can make 

sense and be correct, even though they are not generalized or made formal until later grades. 

Later, students learn to determine domains to which an argument applies. Students at all grades 

can listen or read the arguments of others, decide whether they make sense, and ask useful 

questions to clarify or improve the arguments. 

Consistent with a focus on reasoning and sense-making is a focus on critical reasoning – 

argumentation and critique of arguments. In Pearson’s Scott Foresman • Addison Wesley 

enVisionMATH California, the Interactive Learning affords students opportunities to share 

with classmates their thinking about problems, their solutions, and their reasoning about the 

solutions. The many Reasoning exercises found throughout the program specifically call for 

students to justify or explain their solutions. The Writing to Explain exercises help students 

develop foundational critical reasoning skills by having them construct explanations for 

processes. Articulating clearly an explanation for a process is a stepping stone to critical analysis 

and reasoning of both their own processes and those of others. 

Throughout the program; for examples, see Grade 4 Lessons 5-6, 7-5, 11-8, 14-5, 16-11 

9

Grade 4 


4 Model with mathematics. 

Mathematically proficient students can apply the mathematics they know to solve problems arising 

in everyday life, society, and the workplace. In early grades, this might be as simple as writing an 

addition equation to describe a situation. In middle grades, a student might apply proportional 

reasoning to plan a school event or analyze a problem in the community. By high school, a student 

might use geometry to solve a design problem or use a function to describe how one quantity of 

interest depends on another. Mathematically proficient students who can apply what they know 

are comfortable making assumptions and approximations to simplify a complicated situation, 

realizing that these may need revision later. They are able to identify important quantities in a 

practical situation and map their relationships using such tools as diagrams, two-way tables, graphs, 

flowcharts and formulas. They can analyze those relationships mathematically to draw conclusions. 

They routinely interpret their mathematical results in the context of the situation and reflect on 

whether the results make sense, possibly improving the model if it has not served its purpose. 

Students in Pearson’s Scott Foresman • Addison Wesley enVisionMATH California, are 

introduced to mathematical modeling in the early grades. They first use manipulatives and 

drawings and then equations to model addition and subtraction situations. The Visual 

Learning Bridge and Visual Learning Animation often present real-world situations and 

students are shown how these can be modeled mathematically. In later years, students expand 

their modeling skills to include other graphical representations such as tables, graphs, as well as 

equations. 


9-1, 9-5, 10-5, 11-4, 12-1, 12-2, 12-5, 12-6, 12-9, 13-1, 13-2, 13-5, 13-7, 14-11, 15-5, 16-1, 16-2, 16-6 

5 Use appropriate tools strategically. 

Mathematically proficient students consider the available tools when solving a mathematical 

problem. These tools might include pencil and paper, concrete models, a ruler, a protractor, a 

calculator, a spreadsheet, a computer algebra system, a statistical package, or dynamic geometry 

software. Proficient students are sufficiently familiar with tools appropriate for their grade or 

course to make sound decisions about when each of these tools might be helpful, recognizing both 

the insight to be gained and their limitations. For example, mathematically proficient high school 

students analyze graphs of functions and solutions generated using a graphing calculator. They 

detect possible errors by strategically using estimation and other mathematical knowledge. When 

making mathematical models, they know that technology can enable them to visualize the results 

of varying assumptions, explore consequences, and compare predictions with data. Mathematically 

proficient students at various grade levels are able to identify relevant external mathematical 

resources, such as digital content located on a website, and use them to pose or solve problems. 

They are able to use technological tools to explore and deepen their understanding of concepts. 

Students become fluent in the use of a wide assortment of tools ranging from physical objects, 

including manipulatives, rulers, protractors, and even pencil and paper, to technological tools, 

such as etools, calculators and computers. As students become more familiar with the tools 

available to them, they are able to begin making decisions about which tools are more 

appropriate to solve different kinds of problems. 


5-3, 6-1, 6-6, 8-1, 8-3, 9-4, 10-3, 10-6, 11-2, 13-9, 14-1, 14-6, 15-1, 16-5, 16-10 

10

Grade 4 


6 Attend to precision. 

Mathematically proficient students try to communicate precisely to others. They try to use clear 

definitions in discussion with others and in their own reasoning. They state the meaning of the 

symbols they choose, including using the equal sign consistently and appropriately. They are careful 

about specifying units of measure, and labeling axes to clarify the correspondence with quantities 

in a problem. They calculate accurately and efficiently, express numerical answers with a degree of 

precision appropriate for the problem context. In the elementary grades, students give carefully 

formulated explanations to each other. By the time they reach high school they have learned to 

examine claims and make explicit use of definitions. 

Students are expected to use mathematical terms and symbols with precision. Key terms and 

concepts are highlighted in each lesson. In the Do You Understand feature, students often 

revisit these key terms and provide explicit definitions or explanations of the terms. For the 

Writing to Explain and Think About a Process exercises, students are to provide clear 

explanations of terms, concepts, or processes and to use new terms accurately and precisely. 

Students are reminded to use appropriate units of measure when working through solutions 

and accurate labels on axes when making graphs to represent solutions. 


10-6, 11-1, 11-2, 13-9, 14-1, 14-6, 15-1, 16-5, 16-6, 16-10 

7 Look for and make use of structure. 

Mathematically proficient students look closely to discern a pattern or structure .Young students, 

for example, might notice that three and seven more is the same amount as seven and three more, 

or they may sort a collection of shapes according to how many sides the shapes have. Later, 

students will see 7 × 8 equals the well remembered 7 × 5 × 7 × 3, in preparation for learning about 

the distributive property. In the expression x 2 + 9x + 14, older students can see the 14 as 2 × 7 and 

the 9 as 2 + 7.They recognize the significance of an existing line in a geometric figure and can use 

the strategy of drawing an auxiliary line for solving problems. They also can step back for an 

overview and shift perspective. They can see complicated things, such as some algebraic expressions, 

as single objects or as being composed of several objects. For example, they can see 5 3(x y) 2 as 5 

minus a positive number times a square and use that to realize that its value cannot be more than 5 

for any real numbers x and y. 

Throughout the program, students are encouraged to look for structure as they develop solution 

plans. In the Look for a Pattern Problem-Solving lessons, children in the early years develop a 

sense of patterning with visual and physical objects. 

As students mature in their mathematical thinking, they look for structure in numerical 

operations by focusing on place value and properties of operations. From this focus on looking 

for and recognizing structure, students become well-equip to draw from patterns to formalize 

their thinking about the structure of operations. 


4-1, 4-2, 4-3, 4-4, 4-5, 5-1, 5-2, 5-3, 5-4, 5-5, 6-1, 6-2, 6-3, 6-4, 6-5, 7-1, 7-2, 7-3, 7-4, 8-1, 8-4, 9-1, 

9-2, 9-4, 9-5, 10-4, 11-1, 11-3, 11-4, 11-7, 12-1, 12-3, 12-4, 12-7, 12-8, 12-9, 13-4, 13-5, 13-6, 13-7, 

13-8, 13-9, 14-2, 14-3, 14-4, 14-8, 14-9, 14-10, 16-1, 16-2, 16-7, 16-8, 16-9 

11

Grade 4 


8 Look for and express regularity in repeated reasoning. 

Mathematically proficient students notice if calculations are repeated, and look both for general 

methods and for shortcuts. Upper elementary students might notice when dividing 25 by 11 that 

they are repeating the same calculations over and over again, and conclude they have a repeating 

decimal. By paying attention to the calculation of slope as they repeatedly check whether points are 

on the line through (1, 2) with slope 3, middle school students might abstract the equation (y – 2)/(x 

– 1) = 3. Noticing the regularity in the way terms cancel when expanding (x – 1)(x + 1), (x – 1)(x 2 + x 

+ 1), and (x – 1)(x 3 + x 2 + x + 1) might lead them to the general formula for the sum of a geometric 

series. As they work to solve a problem, mathematically proficient students maintain oversight of 

the process, while attending to the details. They continually evaluate the reasonableness of their 

intermediate results. 

Once again, throughout the program as a whole, students are prompted to look for repetition in 

computations to derive shortcuts that can make the problem-solving process more efficient. 

Students are prompted to think about problems they encountered previously that may share 

features or processes. They are encouraged to draw on the solution plan developed for that 

problem, and as their mathematical thinking matures, to look for generalizations that can be 

applied to other problem situations. The Interactive Learning activities offer students 

opportunities to look for regularity in the way operations behave. 

Throughout the program; for examples, see \ Grade 4 Lessons 1-5, 1-7, 4-3, 4-4, 4-5, 5-2, 7-2, 9-2, 

9-5. 

12

Grade 4 


to enVisionMATH California 

Correlation of California’s Common Core 

Content Standards 

enVisionMATH® California Grade 4 

The following shows the alignment of enVisionMATH California Grade 4 ©2009 to California‘s 

Common Core Content Standards for Mathematics –– Grade 4. Included in this correlation are 

the supplemental lessons that will be available as part of the transitional support that Pearson is 

providing. These lessons will be available in July 2011 in the Guide to Implementing California’s 

Common Core Content Standards for Mathematics with enVisionMATH California. 

California’s Common Core Content Standards for Mathematics 

Grade 4 

Operations and Algebraic Thinking 

Use the four operations with whole numbers to solve problems. 

4.OA.1 Interpret a multiplication equation as a comparison, e.g., interpret 35 

= 5 × 7 as a statement that 35 is 5 times as many as 7 and 7 times as 

many as 5. Represent verbal statements of multiplicative comparisons 

as multiplication equations. 

4.OA.2 

4.OA.3 

Multiply or divide to solve word problems involving multiplicative 

comparison, e.g., by using drawings and equations with a symbol for 

the unknown number to represent the problem, distinguishing 

multiplicative comparison from additive comparison. 

Solve multistep word problems posed with whole numbers and having 

whole-number answers using the four operations, including problems 

in which remainders must be interpreted. Represent these problems 

using equations with a letter standing for the unknown quantity. 

Assess the reasonableness of answers using mental computation and 

estimation strategies including rounding and explain why a rounded 

solution is appropriate. 

Gain familiarity with factors and multiples. 

4.OA.4 

Find all factor pairs for a whole number in the range 1–100. Recognize 

that a whole number is a multiple of each of its factors. Determine 

whether a given whole number in the range 1–100 is a multiple of a 

given one-digit number. Determine whether a given whole number in 

the range 1–100 is prime or composite. 

Generate and analyze patterns. 

4.OA.5 

Generate a number or shape pattern that follows a given rule. Identify 

apparent features of the pattern that were not explicit in the rule 

itself. 

enVisionMATH 

California ©2009 

Lessons 

3-1, 3-3 

3-1, 3-9 

1-5, 2-1, 2-2, 2-3, 2-4, 

2-5, 4-8, 5-1, 5-2, 5-4, 

6-1, 6-2, 6-3a, 7-1, 7- 

2, 7-3a, 7-3, 7-11, 13- 

1, 13-2, 13-3, 13-4, 

13-5 

3-2, 3-4, 7-9, 7-10 

3-2, 15-8 

13

Grade 4 




Grade 4 

Number and Operations in Base Ten 1 

Generalize place value understanding for multi-digit whole numbers. 

4.NBT.1 

4.NBT.2 

4.NBT.3 

Recognize that in a multi-digit whole number, a digit in one place 

represents ten times what it represents in the place to its right. 

Read and write multi-digit whole numbers using base-ten numerals, 

number names, and expanded form. Compare two multi-digit 

numbers based on meanings of the digits in each place, using >, =, 

and < symbols to record the results of comparisons. 

Use place value understanding to round multi-digit whole numbers 

to any place. 

enVisionMATH 


Lessons 

1-3a, 1-4 

1-1, 1-2, 1-3a 

2-4, 4-2, 4-3, 4-8 

Use place value understanding and properties of operations to perform multi-digit arithmetic. 

4.NBT.4 

4.NBT.5 

4.NBT.5.1 

4.NBT.6 

Fluently add and subtract multi-digit whole numbers using the 

standard algorithm. 

Multiply a whole number of up to four digits by a one-digit whole 

number, and multiply two two-digit numbers, using strategies based 

on place value and the properties of operations. Illustrate and 

explain the calculation by using equations, rectangular arrays, 

and/or area models. 

Solve problems involving multiplication of multi-digit numbers by 

two-digit numbers. (NS.3.3) 

Find whole-number quotients and remainders with up to four-digit 

dividends and one-digit divisors, using strategies based on place 

value, the properties of operations, and/or the relationship between 

multiplication and division. Illustrate and explain the calculation by 

using equations, rectangular arrays, and/or area models. 

2-6, 2-7, 2-8, 2-9 

4-1, 4-2, 4-3, 4-4, 4-5, 

4-6, 4-7, 4-8 

6-1, 6-3a, 6-3, 6-4, 6- 

5, 6-6 

7-3b, 7-3, 7-4, 7-5, 7- 

6, 7-7a, 7-7, 7-8 

1 

(Grade 4 expectations in this domain are limited to whole numbers less than or equal to 1,000,000.) 

14

Grade 4 




Grade 4 

enVisionMATH 


Lessons 

Number and Operations—Fractions 2 

Extend understanding of fraction equivalence and ordering. 

4.NF.1 Explain why a fraction a/b is equivalent to a fraction (n × a)/(n × b) 

by using visual fraction models, with attention to how the number 

and size of the parts differ even though the two fractions 

themselves are the same size. Use this principle to recognize and 

generate equivalent fractions. 

9-3, 9-4a, 9-4, 9-8 

4.NF.2 

Compare two fractions with different numerators and different 

denominators, e.g., by creating common denominators or 

numerators, or by comparing to a benchmark fraction such as 1/2. 

Recognize that comparisons are valid only when the two fractions 

refer to the same whole. Record the results of comparisons with 

symbols >, =, or 1 as a sum of fractions 1/b. 10-1a, 10-1, 10-4 

4.NF.3.a 

4.NF.3.b 

4.NF.3.c 

4.NF.3.d 

4.NF.4 

Understand addition and subtraction of fractions as joining and 

separating parts referring to the same whole. 

Decompose a fraction into a sum of fractions with the same 

denominator in more than one way, recording each decomposition 

by an equation. Justify decompositions, e.g., by using a visual 

fraction model. 

Add and subtract mixed numbers with like denominators, e.g., by 

replacing each mixed number with an equivalent fraction, and/or by 

using properties of operations and the relationship between 

addition and subtraction. 

Solve word problems involving addition and subtraction of fractions 

referring to the same whole and having like denominators, e.g., by 

using visual fraction models and equations to represent the 

problem. 

Apply and extend previous understandings of multiplication to 

multiply a fraction by a whole number. 

10-1 

9-5, 10-1a, 10-3a 

10-3a, 10-3b, 10-4a, 

10-4 

10-1 

10-4c 

4.NF.4.a Understand a fraction a/b as a multiple of 1/b. 10-4b 

4.NF.4.b 

Understand a multiple of a/b as a multiple of 1/b, and use this 

understanding to multiply a fraction by a whole number. 

4.NF.4.c Solve word problems involving multiplication of a fraction by a 10-4d 

10-4c, 10-4d 

2 

(Grade 4 expectations in this domain are limited to fractions with denominators 2, 3, 4, 5, 6, 8, 10, 12, and 100.) 

15

Grade 4 




Grade 4 

whole number, e.g., by using visual fraction models and equations 

to represent the problem. 

Understand decimal notation for fractions, and compare decimal fractions. 

4.NF.5 

Express a fraction with denominator 10 as an equivalent fraction 

with denominator 100, and use this technique to add two fractions 

with respective denominators 10 and 100. 

enVisionMATH 


Lessons 

11-3, 11-4, 11-5a 

4.NF.6 Use decimal notation for fractions with denominators 10 or 100 11-3, 11-4, 11-5a, 

11-5 

4.NF.7 

Compare two decimals to hundredths by reasoning about their size. 

Recognize that comparisons are valid only when the two decimals 

refer to the same whole. Record the results of comparisons with the 

symbols >, =, or

Grade 4 




Grade 4 

Measurement and Data 

enVisionMATH 


Lessons 

Solve problems involving measurement and conversion of measurements from a larger unit to a smaller 

unit. 

4.MD.1 

4.MD.2 

4.MD.3 

Know relative sizes of measurement units within one system of units 

including km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec. Within a single 

system of measurement, express measurements in a larger unit in 

terms of a smaller unit. Record measurement equivalents in a twocolumn 

table. 

Use the four operations to solve word problems involving distances, 

intervals of time, liquid volumes, masses of objects, and money, 

including problems involving simple fractions or decimals, and 

problems that require expressing measurements given in a larger 

unit in terms of a smaller unit. Represent measurement quantities 

using diagrams such as number line diagrams that feature a 

measurement scale. 

Apply the area and perimeter formulas for rectangles in real world 

and mathematical problems. 

Represent and interpret data. 

4.MD.4 

Make a line plot to display a data set of measurements in fractions 

of a unit (1/2, ¼, 1/8). Solve problems involving addition and 

subtraction of fractions by using information presented in line plots. 

Geometric measurement: understand concepts of angle and measure angles. 

4.MD.5 

4.MD.5.a 

4.MD.5.b 

4.MD.6 

4.MD.7 

Recognize angles as geometric shapes that are formed wherever two 

rays share a common endpoint, and understand concepts of angle 

measurement: 

An angle is measured with reference to a circle with its center at the 

common endpoint of the rays, by considering the fraction of the 

circular arc between the points where the two rays intersect the 

circle. An angle that turns through 1/360 of a circle is called a “onedegree 

angle,” and can be used to measure angles. 

An angle that turns through n one-degree angles is said to have an 

angle measure of n degrees. 

Measure angles in whole-number degrees using a protractor. Sketch 

angles of specified measure. 

Recognize angle measure as additive. When an angle is decomposed 

into non-overlapping parts, the angle measure of the whole is the 

sum of the angle measures of the parts. Solve addition and 

subtraction problems to find unknown angles on a diagram in real 

world and mathematical problems, e.g., by using an equation with a 

symbol for the unknown angle measure. 

15-1, 15-2a, 15-2, 

15-3a 

10-4, 12-5a, 12-6, 15- 

3b 

15-3, 15-4, 15-5, 

15-6a 

15-3c, 16-3 

8-2, 8-3a 

8-3a, 8-3b 

8-3b, 8-3c 

8-3c 

8-3c 

17

Grade 4 




Grade 4 

Geometry 

enVisionMATH 


Lessons 

Draw and identify lines and angles, and classify shapes by properties of their lines and angles. 

4.G.1 

4.G.2 

4.G.3 

Draw points, lines, line segments, rays, angles (right, acute, obtuse), 

and perpendicular and parallel lines. Identify these in twodimensional 

figures. 

Classify two-dimensional figures based on the presence or absence 

of parallel or perpendicular lines, or the presence or absence of 

angles of a specified size. Recognize right triangles as a category, 

and identify right triangles. (Two dimensional shapes should include 

special triangles, e.g., equilateral, isosceles, scalene, and special 

quadrilaterals, e.g., rhombus, square, rectangle, parallelogram, 

trapezoid.) 

Recognize a line of symmetry for a two-dimensional figure as a line 

across the figure such that the figure can be folded along the line 

into matching parts. Identify line-symmetric figures and draw lines 

of symmetry. 

8-1, 8-2, 8-3a, 8-3b 

8-3, 8-4, 8-5 

19-2 

18

Grade 4 

Pacing for a Common Core Curriculum 


with enVisionMATH® California 

Grade 4 

This pacing chart is provided to help you plan your course as you look 

to implement California’s Common Core Content Standards for 

Mathematics with enVisionMATH California ©2009 in your math 

classroom. The chart indicates the content standard(s) that each 

lesson addresses and proposes pacing for each topic. Included in 

the chart are supplemental lessons that offer in-depth coverage of 

certain standards. These lessons, indicated in dark red, in addition 

to the lessons in the Student Edition provide complete coverage of 

all of the California’s Common Core Content Standards for 

Mathematics –– Grade 4. 

The suggested number of days for each chapter is based on a 45- 

minute class period. The total of 160 days of instruction allows time 

for all of the lessons that address the California Common Core State 

Standards as well as some review and enrichment lessons. 

Content to meet the 

California’s Common Core 

Content Standards for 

Mathematics – Grade 4 

Content from earlier years to 

review and practice 

Content to prepare for future 

study or to enrich the 

curriculum 

Standard(s) for 

Mathematical 

Content 

Topic 1 Numeration 

8 days 

1-1 Thousands 4.NBT.2 

1-2 Millions 4.NBT.2 

1-3a Place Value Relationships 4.NBT.1, 4.NBT.2 

1-3 Comparing and Ordering Whole Numbers 4.NBT.2 

1-4 Understanding Zeros in Place Value 4.NBT.1 

1-5 Problem Solving: Make an Organized List 4.OA.3 

19

Grade 4 



Mathematical 


Topic 2 Addition and Subtraction Number Sense 

11 days 

2-1 Understanding Rounding 4.OA.3 

2-2 Rounding Whole Numbers 4.OA.3 

2-3 Using Mental Math to Add and Subtract 4.OA.3 

2-4 Estimating Sums and Differences of Whole Numbers 4.NBT.3, 4.OA.3 

2-5 Problem Solving: Missing or Extra Information 4.OA.3 

2-6 Adding Whole Numbers 4.NBT.4 

2-7 Subtracting Whole Numbers 4.NBT.4 

2-8 Subtracting Across Zeros 4.NBT.4 

2-9 Problem Solving: Draw a Picture and Write an Equation 4.NBT.4 

Topic 3: Multiplication and Division Meanings and Facts 

12 days 

3-1 Meanings of Multiplication 4.OA.1, 4.OA.2 

3-2 Patterns for Facts 4.OA.4, 4.OA.5 

3-3 Multiplication Properties 4.OA.1 

3-4 3, 4, 6, 7, and 8 as Factors 4.OA.4 

3-5 Problem Solving: Look for a Pattern 4.OA.5 

3-6 Meanings of Division 4.NBT.6 

3-7 Relating Multiplication and Division 4.NBT.6 

3-8 Special Quotients 4.NBT.6 

3-9 Using Multiplication Facts to Find Division Facts 4.OA.2 

3-10 Problem Solving: Draw a Picture and Write an Equation 4.NBT.6 

20

Grade 4 



Mathematical 


Topic 4: Multiplying by 1-Digit Numbers 

10 days 

4-1 Multiplying by Multiples of 10 and 100 4.NBT.5 

4-2 Using Mental Math to Multiply 

4.NBT.3, 4.NBT.5, 

4.OA.3 

 

4-3 Using Rounding to Estimate 4.NBT.3, 4.NBT.5 

4-4 Using an Expanded Algorithm 4.NBT.5 

4-5 Multiplying 2-Digit by 1-Digit Numbers 4.NBT.5 


4-7 Multiplying Greater Numbers by 1-Digit Numbers 4.NBT.5 

4-8 Problem Solving: Reasonableness 

Topic 5: Variables and Expressions 

4.OA.3, 4.NBT.3, 

4.NBT.5 

 

1–4 days 

5-1 Variables and Expressions 4.OA.3 

5-2 Equality 

5-3 Expressions with Parentheses 

5-4 Simplifying Expressions 

5-5 Problem Solving: Act It Out and Use Reasoning 

21

Grade 4 



Mathematical 


Topic 6: Multiplying by 2-Digit Numbers 

10 days 

6-1 Using Mental Math to Multiply 2-Digit Numbers 4.OA.3, 4.NBT.5 

6-2 Estimating Products 4.OA.3 

6-3a Using Compatible Numbers to Estimate 4.NBT.5, 4.OA.3 

6-3 Arrays and an Expanded Algorithm 4.NBT.5 

6-4 Multiplying 2-Digit Numbers by Multiples of Ten 4.NBT.5 


6-6 Multiplying Greater Numbers by 2-Digit Numbers 4.NBT.5 

6-7 Problem Solving: Two-Question Problems 4.OA.3 

Topic 7: Dividing by 1-Digit Divisors 

16 days 

7-1 Using Mental Math to Divide 4.OA.3 

7-2 Estimating Quotients 4.OA.3 

7-3a Estimating Quotients for Greater Dividends 4.OA.3 

7-3b Using Objects to Divide: Division as Repeated Subtraction 4.NBT.6 

7-3 Dividing with Remainders 4.OA.3, 4.NBT.6 

7-4 Connecting Models and Symbols 4.NBT.6 

7-5 Dividing 2-Digit by 1-Digit Numbers 4.NBT.6 

7-6 Dividing 3-Digit by 1-Digit Numbers 4.NBT.6 

7-7a Dividing 4-Digit by 1-Digit Numbers 4.NBT.6 

7-7 Deciding Where to Start Dividing 4.NBT.6 

7-8 Zeros in the Quotient 4.NBT.6 

7-9 Factors 4.OA.4 

7-10 Prime and Composite Numbers 4.OA.4 

7-11 Problem Solving: Multiple-Step Problems 4.OA.3 

22

Grade 4 



Mathematical 


Topic 8: Lines, Angles, and Shapes 

13 days 

8-1 Points, Lines, and Planes 4.G.1 

8-2 Line Segments, Rays, and Angles 4.MD.5, 4.G.1 

8-3a Understanding Angles and Unit Angles 

8-3b Measuring with Unit Angles 

8-3c Adding and Subtracting Angle Measures 

4.MD.5, 4.MD.5.a, 

4.G.1, 

4.MD.5.a, 4.MD.5.b, 

4.G.1 

4.MD.5.b, 4.MD.6, 

4.MD.7 

 

 

 

8-3 Polygons 4.G.2 

8-4 Triangles 4.G.2 

8-5 Quadrilaterals 4.G.2 

8-6 Circles Reviews 4.MD.5.a 

8-7 Solids Prepares for 5.MD.5.c 

8-8 Views of Solids: Nets Prepares for 5.MD.5.c 

8-9 Views of Solids: Perspective 

8-10 Problem Solving: Make and Test Generalizations 4.OA.5, 4.G.2 

23

Grade 4 



Mathematical 


Topic 9: Fraction Meanings and Concepts 

11 days 

9-1 Regions and Sets Reviews 3.NF.1 

9-2 Fractions and Division Prepares for 5.NF.3 

9-3 Equivalent Fractions 4.NF.1 

9-4a Number Lines and Equivalent Fractions 4.NF.1, 4.NF.2 

9-4 Fractions in Simplest Form 4.NF.1 

9-5 Improper Fractions and Mixed Numbers 4.NF.3.b 

9-6 Comparing Fractions 4.NF.2 

9-7 Ordering Fractions 4.NF.2 

9-8 Problem Solving: Writing to Explain 4.NF.1, 4.NF.2 

Topic 10: Addition and Subtraction of Fractions 

12 days 

10-1a Composing and Decomposing Fractions 4.NF.3, 4.NF.3.b 

10-1 

Adding and Subtracting Fractions with Like 

Denominators 

4.NF.3, 4.NF.3.a, 

4.NF.3.d 

 

10-2 Adding Fractions with Unlike Denominators Previews 5.NF.1 

10-3a Modeling Addition and Subtraction of Mixed Numbers 4.NF.3.b, 4.NF.3.c 

10-3b Adding Mixed Numbers 4.NF.3.c 

10-3 Subtracting Fractions with Unlike Denominators Previews 5.NF.1 

10-4a Subtracting Mixed Numbers 4.NF.3.c 

10-4b Fractions as Multiples of Unit Fractions: Using Models 4.NF.4.a 

10-4c Multiplying a Fraction by a Whole Number: Using Models 4.NF.4, 4.NF.4.b 

10-4d 

Multiplying a Fraction by a Whole Number: Using 

Symbols 

4.NF.4.b, 4.NF.4.c 

 

10-4 Problem Solving: Draw a Picture and Write an Equation 

4.NF.3, 4.NF.3.c, 

4.MD.2 

 

24

Grade 4 



Mathematical 


Topic 11: Fraction and Decimal Concepts 

9 days 

11-1 Decimal Place Value Prepares for 4.NF.7 

11-2 Comparing and Ordering Decimals 4.NF.7 

11-3 Fractions and Decimals 4.NF.5, 4.NF.6 

11-4 Fractions and Decimals on the Number Line 4.NF.5, 4.NF.6 

11-5a Equivalent Fractions and Decimals 4.NF.5, 4.NF.6 

11-5 Mixed Numbers and Decimals on the Number Line 

Extends 4.NF.5, 

4.NF.6 

 

11-6 Problem Solving: Use Objects and Make a Table 

Topic 12: Operations with Decimals 

1–5 days 

12-1 Rounding Decimals Previews 5.NBT.4 

12-2 Estimating Sums and Differences of Decimals Prepares for 5.NBT.7 

12-3 Modeling Addition and Subtraction of Decimals Prepares for 5.NBT.7 

12-4 Adding and Subtracting Decimals Prepares for 5.NBT.7 

12-5a Solving Problems Involving Money 4.MD.2 

12-5 Multiplying and Dividing with Decimals Prepares for 5.NBT.7 

12-6 Problem Solving: Try, Check, and Revise 4.MD.2 

Topic 13: Solving Equations 

7 days 

13-1 Equal or Not Equal 4.OA.3 

13-2 Solving Addition and Subtraction Equations 4.OA.3 

13-3 Solving Multiplication and Division Equations 4.OA.3 

13-4 Translating Words to Equations 4.OA.3 

13-5 Problem Solving: Work Backward 4.OA.3 

25

Grade 4 



Mathematical 


Topic 14: Integers 

0–4 days 

14-1 Understanding Integers Prepares for 6.NS.6 

14-2 Comparing Integers Prepares for 6.NS.7 

14-3 Ordering Integers Prepares for 6.NS.7 

14-4 Problem Solving: Draw a Picture 

Prepares for 6.NS.6, 

6.NS. 7 

 

Topic 15: Measurement, Perimeter, and Area 

14 days 

15-1 Customary Measures 4.MD.1 

15-2a Changing Customary Units 4.MD.1 

15-2 Metric Measures 4.MD.1 

15-3a Changing Metric Units 4.MD.1 

15-3b Solving Measurement Problems 4.MD.2 

15-3c Solving Measurement Problems Using Line Plots 4.MD.4 

15-3 Perimeter 4.MD.3 

15-4 Area of Squares and Rectangles 4.MD.3 

15-5 Area of Irregular Shapes Extends 4.MD.3 

15-6a Solving Perimeter and Area Problems 4.MD.3 

15-6 Same Perimeter, Different Area Reviews 3.MD.8 

15-7 Same Area, Different Perimeter Reviews 3.MD.8 

15-8 

Problem Solving: Solve a Simpler Problem and Make a 

Table 

4.OA.5 

 

26

Grade 4 



Mathematical 


Topic 16: Data and Graphs 

2–6 days 

16-1 Data from Surveys Prepares for 6.SP.1 

16-2 Interpreting Graphs Reviews 3.MD.3 

16-3 Line Plots 4.MD.4 

16-4 Mean Prepares for 6.SP.3 

16-5 Median, Mode, and Range Prepares for 6.SP.3 

16-6 Problem Solving: Make a Graph Reviews 3.MD.3 

Topic 17: Length and Coordinates 

0–4 days 

17-1 Ordered Pairs Prepares for 5.G.1 

17-2 Shapes on Coordinate Grids Prepares for 6.G.3 

17-3 Lengths of Horizontal and Vertical Line Segments Prepares for 6.G.3 

17-4 Problem Solving: Solve a Simpler Problem 

Topic 18: Formulas and Equations 

0–6 days 

18-1 Formulas and Equations Extends 4.MD.3 

18-2 Addition and Subtraction Patterns and Equations Prepares for 5.OA.3 

18-3 Multiplication and Division Patterns and Equations Prepares for 5.OA.3 

18-4 Graphing Equations Prepares for 5.OA.3 

18-5 More Graphing Equations Prepares for 5.OA.3 

18-6 Problem Solving: Make a Table 

27

Grade 4 



Mathematical 


Topic 19: Congruence and Symmetry 

2–4 days 

19-1 Congruent Figures 

19-2 Line Symmetry 4.G.3 

19-3 Rotational Symmetry Extends 4.G.3 

19-4 Problem Solving: Draw a Picture Extends 4.G.1 

Topic 20: Probability 

0–3 days 

20-1 Finding Combinations 

20-2 Outcomes and Tree Diagrams 

20-3 Writing Probability as a Fraction 

20-4 Problem Solving: Use Reasoning 

28

Grade 4 

Supplemental Common Core Lessons 

Supplemental Common Core Lessons 

enVisionMATH® California Grade 4 

The supplemental lessons listed below will be available in summer 2011. These lessons 

ensure comprehensive coverage of all of California’s Common Core Content Standards 

for Mathematics — Grade 4. 

1-3a Place Value Relationships 

6-3a Using Compatible Numbers to Estimate 

7-3a Estimating Quotients for Greater Dividends 

7-3b Using Objects to Divide: Division as Repeated Subtraction 

7-7a Dividing 4-Digit by 1-Digit Numbers 

8-3a Understanding Angles and Unit Angles 

8-3b Measuring with Unit Angles 

8-3c Adding and Subtracting Angle Measures 

9-4a Number Lines and Equivalent Fractions 

10-1a Composing and Decomposing Fractions 

10-3a Modeling Addition and Subtraction of Mixed Numbers 

10-3b Adding Mixed Numbers 

10-4a Subtraction Mixed Numbers 

10-4b Fractions as Multiples of Unit Fractions: Using Models 

10-4c Multiplying a Fraction by a Whole Number: Using Models 

10-4d Multiplying a Fraction by a Whole Number: Using Symbols 

11-5a Equivalent Fractions and Decimals 

12-5a Solving Problems Involving Money 

15-2a Changing Customary Units 

15-3a Changing Metric Units 

15-3b Solving Measurement Problems 

15-3c Solving Measurement Problems Using Line Plots 

15-6a Solving Perimeter and Area Problems 

29

Transitioning to California's Common Core Content Standards for ...

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